Which one is a better approach
When it comes to game assets there is one general simple rule. Use as many polygons as necessary and as little polygons as possible. No exception.

It's not only the amount of polygons but also the amount of vertices that matter. On top of that you also have to take the amount of UV islands for texturing (that means no "Smart UV Projection" or other fancy UV shortcut nonsense). 

Also, don't assume the performance hit by the size of the object (in terms of screen space) in your finished game, neither the CPU nor the GPU care about that. They only care about the complexity as I described it above. 

Continuous planks and bars (like in your fist example) through other meshes are the way to go, as long as they stay at the same position at their entry and exit points.